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Quadratic Equations

Short Answer Type

61. Represent the following situation in the form of a quadratic equation:
The sum of the ages of a son and his father (in years) is 35 and the product of their ages is 150.

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62. Represent the following situation in the form of a quadratic equation:
The product of Aditya’s age in years, five years ago with his age in years 9 years later is 15.

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63. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.

space space 2 straight x squared minus 4 straight x plus 3 equals 0

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64. Find the discriminant of the following quadratic equation, and hence find the nature of its roots.
$3 straight x squared minus 2 straight x plus 1 third equals 0$

We have,
$3 straight x squared minus 2 straight x plus 1 third equals 0$
Here, $straight a equals 3 comma space straight b equals negative 2 comma space straight c equals 1 third$
Now,
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Since, D = 0
Therefore, the given quadratic equation has equal roots.